Abstract
In the past decade, various types of wavelet-based algorithms were proposed, leading to a key tool in the solution of a number of numerical problems. This work adopts the Chebyshev wavelets for the numerical solution of several models. A Chebyshev operational matrix is developed, for selected collocation points, using the fundamental properties. Moreover, the convergence of the expansion coefficients and an upper estimate for the truncation error are included. The obtained results for several case studies illustrate the accuracy and reliability of the proposed approach.
Highlights
Several algorithms, such as the finite difference and finite element, as well as spectral techniques, have been used in the approximation of mathematical models [1,2,3,4]
The Galerkin and collocation approaches along with wavelets [9,10,11,12] were applied in elasticity problems
This paper presents a new technique for obtaining the numerical spectral solutions for multi-term fractional-order initial value problems
Summary
Several algorithms, such as the finite difference and finite element, as well as spectral techniques, have been used in the approximation of mathematical models [1,2,3,4]. Wavelets have relevant features such as orthogonality, capability of representing functions with different levels of resolution, and the exact representation of polynomials, just to mention a few. Such properties stimulated the development of efficient algorithms based on the Haar, Daubechies, and Legendre wavelets [5,6] that lead to highly stable results [7,8]. Having in mind the properties of wavelet methods, we propose a Chebyshev wavelet algorithm for solving some types of differential equations.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
